Masako Bando

Nonlinear Realization and Hidden Local Symmetries

Abstract The idea of dynamical gauge bosons of hidden local symmetries in nonlinear sigma models is reviewed. Starting with a fresh look at the Goldstone theorem and low energy theorems, we present a modern review of the general theory of nonlinear realization both in nonsupersymmetric and supersymmetric cases. We then show that any nonlinear sigma model based on the manifold G / H is gauge equivalent to a “linear” model possessing a G global × H local symmetry, H local being a hidden local symmetry. The corresponding supersymmetric formulation is also presented. The above gauge equivalence can be extended to a model having a larger symmetry G global × G local . Also reviewed are dynamical calculatio ns showing that in some two-, three- and four-dimensional models, the gauge bosons of the hidden local symmetries acquire the kinetic terms via quantum effects, thus becoming “dynamical”. We suggest that such a dynamical gauge boson may be a rather common phenomenon realized in Nature. As a realistic example, we examine the QCD case where we identify the vector mesons (ϱ,ω,ф,K ∗ ) with the dynamical gauge bosons of the hidden U(3) v local symmetry in the U(3) L × U(3) R /U(3) V nonlinear sigma model. The totality of the vector meson phenomenology seems to support our basic idea. The axial-vector mesons are also incorporated into our framework. Also given is a brief sketch of some applications of this formalism to unified models beyond the standard model, such as technicolor, composite W/Z boson and supergravity models.

On the Vector Mesons as Dynamical Gauge Bosons of Hidden Local Symmetries

We obtain the KSRF relation, gϱ/gϱππ = 2ƒπ2, as a “low-energy theorem” of the hidden local symmetry in the U(3)L × U(3)R/U(3)v nonlinear sigma model, which proves to be clear evidence of vector mesons being dynamical gauge bosons of the hidden local symmetry. U(3)1 × U(3)R breaking are also discussed, leading to successful relations: gϱ/mϱ2 = 3gω/mω2 = −√123gφ /mφ2=1/g and mφ/mK∗=mK∗/mω=mK∗/mϱ. We further show that it is formally possible to extend the hidden local symmetry so as to incorporate the axial-vector mesons.

Structure stability of congestion in traffic dynamics

In our previous paper, we proposed a dynamical model, whose equation of motion is expressed as a second order differential equation. This model generates traffic congestion spontaneously. In this paper we study the characteristic properties of the traffic congestion in our model, especially the organization process and the stability of the structure of congestion. It turns out that these phenomena are well described by plotting motions of vehicles in the phase space of velocity and headway. The most remarkable feature is the universality of “the hysterisis loop” in this phase space, which is observed in the final stage of the congestion organization. This loop is understood as a limit cycle of the dynamical system. This universality guarantees the stability of total cluster size.

Structure of non-linear realization in supersymmetric theories

Abstract We clarify the origin of massless particles which come out when an internal symmetry breaks down preserving supersymmetry. A special feature is that even if original and final symmetries are fixed, there exist many inequivalent non-linear realizations. We present the theorems which make clear the essential structure of the phenomena. The (non-linear)_transformation law for the massless particles is accurately defined and it is shown how to construct the supersymmetric non-linear lagrangian.

Brane Fluctuations and Suppression of Kaluza-Klein Mode Couplings

In higher dimensional models where the gauge and gravity fields live in the bulk and the matter fields only in a brane, we point out the importance of the brane (transverse) coordinate modes, which are the Nambu-Goldstone bosons appearing as a result of spontaneous breaking of the translation symmetry. The brane recoil effect suppresses the couplings of higher Kaluza-Klein modes to the matter, and gives a natural resolution to the divergence problem caused by the exchange of infinitely many Kaluza-Klein modes.

Improving the effective potential

Abstract A g ene ral procedure is presented how to improve the effective potential by using the renormalization group equation (RGE) in the MS scheme. If one knows the L-loop effective potential and the RGE coefficient functions up to the (L + 1)-loop level, this procedure gives an improved potential which satisfies the RGE and contains all of the leading, nest-to-leading, …, and Lth-to-leading log terms.

Mass Matrices in E6 Unification.

We study a supersymmetric E6 grand unified model in which the SU(5) 5 ∗ components are twisted in the third generation 27. Supplementing the adjoint Higgs field to a model analyzed previously, we calculate the mass matrices for the up and down quarks and charged leptons. Although the number of free parameters is less than that of observables, an overall fitting to the observed masses and mixing angles is shown to be possible. Most notably, we find two novel, parameter-independent relations between the lepton 2-3 mixing angle θμτ and the quark masses and CKM mixing angles that are in good agreement with the large lepton mixing recently observed.

Neutrino Masses in E6 Unification

We show that neutrino masses with large mixing between νμ and ντ are naturally reproduced in a supersymmetric E6 grand unification model with an anomalous U(1)X symmetry. We propose a simple scenario which incorporates a novel mechanism called ‘E-twisting’ by which all the characteristic features of the fermion mass matrices, not only the quark/lepton Dirac masses but also the neutrino’s Majorana masses, can be reproduced despite the fact that all the members in 27 of each generation are assigned a common U(1)X charge.

Improving the Effective Potential Multi-Mass-Scale Case

Previously proposed procedure for improving the effective potential by using renormalization group equation (RGE) is generalized so as to be applicable to any system containing several different mass scales. If one knows L-loop effective potential and (L + 1)-loop RGE coefficient functions, this procedure gives an improved potential which satisfies the RGE and contains all of the leading, next-to-leading,..., and L-th-to-leading log terms. Our procedure here also clarifies how naturally the so-called effective field theory can be incorporated in the RGE in MS scheme

E6 Unification with Bi-Large Neutrino Mixing

The scenario of SO(10) grand unified theory (GUT) proposed by one of the authors is extended to E 6 unification. This gives realistic quark and lepton mass matrices. In the neutrino sector, the model reproduces the large mixing angle (LMA) MSW solution as well as the large mixing angle for the atmospheric neutrino anomaly. In this model, the right-handed down quark and the left-handed lepton of the first and second generations belong to a single multiplet 27. This causes natural suppression of the flavour changing neutral current (FCNC).